In this thesis work, the background of atmospheric turbulence degradation in imaging was reviewed and two aspects are highlighted: blurring and geometric distortion. The turbulence burring parameter is determined by the atmospheric turbulence condition that is often unknown; therefore, a blur identification technique was developed that is based on a higher order statistics (HOS). It was observed that the kurtosis generally increases as an image becomes blurred (smoothed). Such an observation was interpreted in the frequency domain in terms of phase correlation. Kurtosis minimization based blur identification is built upon this observation. It was shown that kurtosis minimization is effective in identifying the blurring parameter directly from the degraded image. Kurtosis minimization is a general method for blur identification. It has been tested on a variety of blurs such as Gaussian blur, out of focus blur as well as motion blur. To compensate for the geometric distortion, earlier work on the turbulent motion compensation was extended to deal with situations in which there is camera/object motion. Trajectory smoothing is used to suppress the turbulent motion while preserving the real motion. Though the scintillation effect of atmospheric turbulence is not considered separately, it can be handled the same way as multiple frame denoising while motion trajectories are built.

Bachelor-Arbeit Univ. St. Gallen, 2008.

The purpose of this thesis is to propose some test statistics for testing the skewness and kurtosis parameters of a distribution, not limited to a normal distribution. Since a theoretical comparison is not possible, a simulation study has been conducted to compare the performance of the test statistics. We have compared both parametric methods (classical method with normality assumption) and non-parametric methods (bootstrap in Bias Corrected Standard Method, Efron’s Percentile Method, Hall’s Percentile Method and Bias Corrected Percentile Method). Our simulation results for testing the skewness parameter indicate that the power of the tests differs significantly across sample sizes, the choice of alternative hypotheses and methods we chose. For testing the kurtosis parameter, the simulation results suggested that the classical method performs well when the data are from both normal and beta distributions and bootstrap methods are useful for uniform distribution especially when the sample size is large.

Kurtosis can be measured in more than one way. A modification of Geary's measure of kurtosis is shown to be more sensitive to kurtosis in the center of the distribution while Pearson's measure of kurtosis is more sensitive to kurtosis in the tails of the distribution. The modified Geary measure and the Pearson measure are used to define a joint test of kurtosis that has high uniform power across a very wide range of symmetric nonnormal distributions.

Nonnormality in the form of skewness and kurtosis was examined in lot acceptance quality characteristics data from seven state highway agencies for their highway construction quality assurance programs. Lot skewness and kurtosis varied significantly. For most lot data sets, skewness values varied in the range of 0.0 ± 1.0, whereas most kurtosis values varied in the range of 0.0 ± 2.0. The analysis also reveals that, on average, 50% of lot test data sets were nonnormal with 15% of lot data sets having skewness greater than ±1.0 and kurtosis greater than ±2.0. This is a significant finding because most state transportation agencies' pay factor algorithms assume normally distributed lot. Further investigation showed that high skewness and kurtosis were associated with higher lot variability. This variability produced misleading results in regard to inflated Type I error and low power for the F-test. However, the t-test was found to be quite robust for distinguishing mean differences. Significant deviation was observed in lot pay factors based on percent within limits between assumed normal data and normalized data. Effects of nonnormal distribution on the lot pay factor were found to be varied on the basis of the specification limits, the distribution of defective materials on the tails in the case of two-sided limits, and the orientation of the nonnormal distribution itself.

No / The use of electroencephalograms (EEGs) to diagnose and analyses Alzheimer's disease (AD) has received much attention in recent years. The sample entropy (SE) has been widely applied to the diagnosis of AD. In our study, nine EEGs from 21 scalp electrodes in 3 AD patients and 9 EEGs from 3 age-matched controls are recorded. The calculations show that the kurtoses of the AD patients' EEG are positive and much higher than that of the controls. This finding encourages us to introduce a kurtosis-based de-noising method. The 21-electrode EEG is first decomposed using independent component analysis (ICA), and second sort them using their kurtoses in ascending order. Finally, the subspace of EEG signal using back projection of only the last five components is reconstructed. SE will be calculated after the above de-noising preprocess. The classifications show that this method can significantly improve the accuracy of SE-based diagnosis. The kurtosis analysis of EEG may contribute to increasing the understanding of brain dysfunction in AD in a statistical way.

This thesis includes three chapters regarding influence functions, higher moments, and futures hedging. In Chapter 2, the objective is to use an influence function to better understand semi-kurtosis for use in analyzing peakedness and tail heaviness on one side of a distribution. Also, it is shown that both the right side semi-kurtosis and left side semi-kurtosis summed together, equal kurtosis, so the ratio of semi-kurtosis to kurtosis can be used to analyze asymmetry, as an alternative to skewness. In Chapter 3, the objective is to analyze higher moments of daily, weekly, and monthly stock market returns using large stocks, technology stocks, and small cap stocks. Kurtosis is found to be positive (greater than 3) and statistically significant for all of the daily and weekly stock market returns, indicating peakedness and fat tails. Similar to kurtosis, the left side semi-fourth moment (semi-kurtosis) is also found to be positive (greater than 1.5) for all of daily and weekly returns, indicating peakedness and fat tails on the left sides of the distributions. Skewness is found to be both positive and negative in the daily stock returns data, indicating asymmetry but with no consistent patterns. The fifth moment is also used to analyze asymmetry, as an alternative to skewness. The fifth moment and skewness (third moment) sometimes indicate opposite asymmetry results, as evidenced by different signs for the two moments. This is because the exponent of five for the fifth moment amplifies observations further from the mean, more so than the exponent of three for skewness. In Chapter 4, the objective is to analyze research on futures hedging and to identify the major factors affecting the use of futures hedging by commodity producers. A multifactor conceptual model is developed that explains the factors and subfactors that are likely to affect the commodity producers’ hedging decisions. Factors include industry characteristics, business operation characteristics, management characteristics, futures hedging costs, and substitute risk management instruments. This model provides a more complete understanding of the factors and subfactors affecting futures hedging, and should be of interest to academics and practitioners working with hedging models.

This thesis includes three chapters regarding influence functions, higher moments, and futures hedging. In Chapter 2, the objective is to use an influence function to better understand semi-kurtosis for use in analyzing peakedness and tail heaviness on one side of a distribution. Also, it is shown that both the right side semi-kurtosis and left side semi-kurtosis summed together, equal kurtosis, so the ratio of semi-kurtosis to kurtosis can be used to analyze asymmetry, as an alternative to skewness. In Chapter 3, the objective is to analyze higher moments of daily, weekly, and monthly stock market returns using large stocks, technology stocks, and small cap stocks. Kurtosis is found to be positive (greater than 3) and statistically significant for all of the daily and weekly stock market returns, indicating peakedness and fat tails. Similar to kurtosis, the left side semi-fourth moment (semi-kurtosis) is also found to be positive (greater than 1.5) for all of daily and weekly returns, indicating peakedness and fat tails on the left sides of the distributions. Skewness is found to be both positive and negative in the daily stock returns data, indicating asymmetry but with no consistent patterns. The fifth moment is also used to analyze asymmetry, as an alternative to skewness. The fifth moment and skewness (third moment) sometimes indicate opposite asymmetry results, as evidenced by different signs for the two moments. This is because the exponent of five for the fifth moment amplifies observations further from the mean, more so than the exponent of three for skewness. In Chapter 4, the objective is to analyze research on futures hedging and to identify the major factors affecting the use of futures hedging by commodity producers. A multifactor conceptual model is developed that explains the factors and subfactors that are likely to affect the commodity producers’ hedging decisions. Factors include industry characteristics, business operation characteristics, management characteristics, futures hedging costs, and substitute risk management instruments. This model provides a more complete understanding of the factors and subfactors affecting futures hedging, and should be of interest to academics and practitioners working with hedging models.

Diffusion of water molecules in biological tissues depends on several microstructural properties. Therefore, diffusion Magnetic Resonance Imaging (dMRI) is a useful tool to infer and study microstructural brain changes in the context of human development, ageing and neuropathology. In this thesis, the state-of-the-art of advanced dMRI techniques is explored and strategies to overcome or reduce its pitfalls are developed and validated. Firstly, it is shown that PCA denoising and Gibbs artefact suppression algorithms provide an optimal compromise between increased precision of diffusion measures and the loss of tissue's diffusion non-Gaussian information. Secondly, the spatial information provided by the diffusion kurtosis imaging (DKI) technique is explored and used to resolve crossing fibres and generalize diffusion measures to cases not limited to well-aligned white matter fibres. Thirdly, as an alternative to diffusion microstructural modelling techniques such as the neurite orientation dispersion and density imaging (NODDI), it is shown that spherical deconvolution techniques can be used to characterize fibre crossing and dispersion simultaneously. Fourthly, free water volume fraction estimates provided by the free water diffusion tensor imaging (fwDTI) are shown to be useful to detect and remove voxels corrupted by cerebrospinal fluid (CSF) partial volume effects. Finally, dMRI techniques are applied to the diffusion data from the large collaborative Cambridge Centre for Ageing and Neuroscience (CamCAN) study. From these data, the inference provided by diffusion anisotropy measures on maturation and degeneration processes is shown to be biased by age-related changes of fibre organization. Inconsistencies of previous NODDI ageing studies are also revealed to be associated with the different age ranges covered. The CamCAN data is also processed using a novel non-Gaussian diffusion characterization technique which is invariant to different fibre configurations. Results show that this technique can provide indices specific to axonal water fraction which can be linked to age-related fibre density changes.

Master of Science / Department of Electrical and Computer Engineering / Steven Warren / Handgrip contractions are a useful exercise for assessing muscle fatigue in the forearm musculature. Most conventional hand-forearm ergometer systems require the researcher to manually guide subject activity, collect subject data, and assess subject fatigue after it has occurred. Since post-processing tools are not standardized for this type of experiment, researchers resort to building their own tools. This process can make comparing results between research groups difficult. This thesis presents updates to a hand-forearm ergometer system that automate the control, data-acquisition, and data-analysis mechanisms. The automated system utilizes a LabVIEW virtual instrument as the system centerpiece; it provides the subject/researcher interfaces and coordinates data acquisition from both traditional and new sensors. The system also processes the hand-forearm data within the LabVIEW environment as the data are collected. This allows the researcher to better understand the onset of subject fatigue while an experiment is in progress. System upgrades relative to prior work include the addition of new parameters to the researcher display, a change in the subject display from a binary up-down display to a sliding bar for better control over subject grip state, and a software update from a simple data acquisition and display system to a real-time processing system. The toolset has proven to be a viable support resource for experimental studies performed in the Kansas State University Human Exercise Physiology Laboratory that target muscle fatigue in human forearms. Initial data acquired during these tests indicate the viability of the system to acquire consistent and physiologically meaningful data while providing a useable toolset for follow-on data analyses.